Poincare-Friedrichs Type Constants for Operators Involving grad, curl,\n and div: Theory and Numerical Experiments

2019/09/25 by Dirk Pauly, Pauly, Dirk, Jan Valdman +1
Mathematics · #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Numerical Analysis (math.NA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1909.11563

openalex publication_date 2019/09/25 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We give some theoretical as well as computational results on Laplace and\nMaxwell constants. Besides the classical de Rham complex we investigate the\ncomplex of elasticity and the complex related to the biharmonic equation and\ngeneral relativity as well using the general functional analytical concept of\nHilbert complexes. We consider mixed boundary conditions and bounded Lipschitz\ndomains of arbitrary topology. Our numerical aspects are presented by examples\nfor the de Rham complex in 2D and 3D which not only confirm our theoretical\nfindings but also indicate some interesting conjectures.\n

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